a brief introduction to magnetic resonance...
TRANSCRIPT
![Page 1: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/1.jpg)
A Brief Introduction to Magnetic Resonance Imaging
Anthony Wolbarst, Kevin King, Lisa Lemen,
Ron Price, Nathan Yanasak
![Page 2: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/2.jpg)
Outline for Today
1) Introduction Wolbarst
MRI Case Study; Caveat!!!
“Quasi-Quantum” Nuclear Magnetic Resonance
2) Net magnetization, m(x,t), of the voxel at x Lemen
T1 Spin-Relaxation of m(x,t),
T1 MRI of the 1D patient
Sketch of the MRI Device
3) ‘Classical’ Approach to NMR Yanasak
FID Image Reconstruction, k-Space
4) Spin-Echo Reconstruction Price
T2 Spin-Relaxation
T1-w, T2-w, and PD-w S-MRI
Spin-Echo / Spin-Warp in 2D
Some Important Topics Not Addressed Here
![Page 3: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/3.jpg)
Magnetic Resonance Imaging:
Mapping the Spatial Distribution
of Spin-Relaxation Rates
of Hydrogen Nuclei
in Soft-Tissue Water and Lipids
![Page 4: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/4.jpg)
Part 1:
“Quasi Quantum”
NMR and MRI
Introduction
MRI Case Study; Caveat!!!
“Quasi-Quantum” NMR and MRI
+
+
+ + +
N
S
µ
J
![Page 5: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/5.jpg)
Introduction
![Page 6: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/6.jpg)
Beam of ‘probes’:
particles or waves
Image receptor
Differential transmission, reflection, emission, etc., of probes
Medical Imaging: differential interactions of probes with different tissues
![Page 7: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/7.jpg)
Forms of Contrast Between Good and Bad Apples produced and detected thru different bio/chemico/physical processes
The Future: Contrast Mechanisms!
Color
Smell
Taste
Texture Holes
etc.
![Page 8: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/8.jpg)
Modality Probe / Signal Detector Source of Contrast: differences in…
Planar R/F X-ray
CT
X-rays passing
through body
II+CCD, AMFPI;
GdO, etc., array µ( ρ, Z, kVp) ds
Nuc Med,
SPECT;
PET
Gamma-rays
from body;
511 keV
NaI single crystal;
multiple NaI;
LSO array
Radiopharmaceutical
uptake, concentration
(e.g., 99mTc), emission
US MHz sound Piezoelectric transducer ρ, κ, µUS
MRI Magnet, RF AM radio receiver T1, T2, PD, [O], blood
flow, water diffusion,
chemical shift
How Imaging Modalities Detect Tissue Contrast…
s
![Page 9: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/9.jpg)
CT MRI
Posterior reversible encephalopathy syndrome (PRES), edematous changes
CT vs. MRI Soft Tissue Contrast
![Page 10: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/10.jpg)
Multiple types of contrast, created through and reflecting
different aspects of soft tissue biophysics.
Selection of contrast type with pulse sequences
Most reflect rotations, flow, etc., of water/lipid molecules;
yield distinct, unique maps of anatomy, physiology
No ionizing radiation
Risks from intense magnetic fields, RF power
Expensive
Technology complex, challenging to learn;
Much of biophysics little understood. But….
Magnetic Resonance Imaging
![Page 11: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/11.jpg)
MRI Case Study; and Caveat!!!
with T1, FLAIR, MRS, DTI, or f MRI contrast
and MR-guided biopsy studies of a glioma
![Page 12: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/12.jpg)
Case Study
57 year old ♀ medical physicist has had daily headaches
for several months. Responds to ½ Advil.
Physical examination unremarkable. Patient appears to
be in good general health, apart from mild hypertension,
controlled by medication.
Good diet, exercises moderately. Patient reports no
major stresses, anxieties.
CT indicates a lesion in the right posterior temporo-
occipital region, adjacent to occipital horn of right
lateral ventricle. MRI for more information.
Principal concern: Vision for reading.
![Page 13: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/13.jpg)
T1-w FLAIR
f MRI
visual stimulus
DTI
No enhancement
with Gd contrast.
Lesion: Right Posterior Temporo-Occipital Region, adjacent to occipital horn of right lateral ventricle
![Page 14: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/14.jpg)
Chemical Shift and Non-invasive MRS
CH3
COOH
Astrocytoma
acetic acid
1.56 ppm
![Page 15: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/15.jpg)
Grade 1-2 Astrocytoma
with scattered cellular pleomorphism and nuclear atypia
MRI-Guided Needle Biopsy
![Page 16: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/16.jpg)
Caveat!!! Extreme Danger
![Page 17: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/17.jpg)
How Not to Clean a Magnet
www.simplyphysics.com
strong gradient fields outside bore
![Page 18: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/18.jpg)
MRI Safety
fringes of principal magnetic field
rapidly switching (gradient) fields
high RF power
FDA: ~ 40 MRI-related accidents/year
70% RF burns, 10% metallic “missiles”
no magnetic anything in or entering MRI room
restricted access, safe zones, prominent warnings
accompany all patients, visitors, non-MRI staff
accurate medical history; double-check for metal
training for any staff (e.g., cleaners)
possible gadolinium risk: nephrogenic systemic fibrosis (NSF)
pregnant patients generally should not have Gd-contrast
RF Specific Absorption Rate (SAR): dE/dm (W/kg)
![Page 19: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/19.jpg)
hemostat, scalpel, syringe
O2 bottle, IV pole
scissors, pen, phone, laptop
tool, tool chest
wheelchair, gurney
ax, fire extinguisher
gun, handcuffs
cleaning bucket, mop
aneurysm clip, shrapnel
cochlear implant, prostheses
artificial heart valve
stent, permanent denture
defibrillator, pacemaker,
electrodes, nerve stimulator
medical infusion pump
drug-delivery patch, tattoo
in / into imaging suite within / with patient, others
MRI Safety – First and Foremost, Restrict Entry!
![Page 20: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/20.jpg)
“Quasi-Quantum” NMR and MRI
Swept-frequency NMR in a tissue voxel
Proton-Density (PD) MRI in the 1D patient
Magnetization, m(x,t), in the voxel at x
![Page 21: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/21.jpg)
quantum spin-state function for hydrogen nucleus
| ψ
Simple QM Classical Bloch Eqs.
|↑ , |↓
transitions between precession, nutation of spin-up-, spin-down states net voxel magnetization, m(t)
fLarmor , m0 , T1 fLarmor , T2 , 2D, k-space oversimplified; exact, for expectation values; like Bohr atom from full QM
Two Approaches to Proton NMR/MRI (incompatible!)
expectation values in voxel
start with this
![Page 22: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/22.jpg)
z
x
‘Open’ MRI Magnet principal magnetic field B0 defines z-axis
B0
S
B0
N
z
![Page 23: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/23.jpg)
Moving Charge Produces Magnetic Field (e.g., mag. dipole);
Magnetic Dipole Tends to Align in External Field
µ
N
S
simplified QM picture
proton
T
Bz
e
mechanical relaxation
+
+
+ + +
N
S
µ
J
![Page 24: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/24.jpg)
º
θ Bz along
z-axis N
Energy to Flip Over Needle with Magnetic Moment μ in Bz
E = – μ • Bz
= – μ Bz cos θ
z
ΔE180º = ± 2 μ Bz
µ
![Page 25: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/25.jpg)
Low-energy state
0
+ μz
North
High-energy state
South
– μz
Bz
E(Bz)
ΔE Bz
N
Nuclear Zeeman Splitting for Proton: ΔE = ± 2 μz Bz μ points only along or against z
![Page 26: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/26.jpg)
Swept-frequency NMR in a tissue voxel
![Page 27: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/27.jpg)
spin flip
Ener
gy
(μ
eV )
fL
arm
or [
MH
z]
Bz (T)
60
40
20
0.2
0.1
0.5 1 1.5
H-1
P-31
Nuclear Magnetic Resonance – μz
+μz
proton ΔE180° = 2 μz Bz
photon E = hf
MHz
T
hfLarmor(Bz) = 2 μz Bz
for water protons,
fLarmor, H O = 42.58 ×Bz
hf
Bz(x) = fLarmor(x) / 42.58
42.58 MHz
63.87 MHz
2
2πfLarmor ≡ ω = γ Bz
T
Orientational
Energy
![Page 28: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/28.jpg)
I-1. For protons, fLarmor = 42.58 MHz
at 1 T. What is it at 1.5 T?
2%
3%
84%
2%
8% a. 42.58 MHz
b. 28.36 MHz
c. 63.87 MHz
d. 21.39 MHz
e. Cannot be determined from this
info.
![Page 29: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/29.jpg)
SAMs Q: I-1. For protons, fLarmor = 42.58 MHz at 1 T. What is it at 1.5 T? (a) 42.58 MHz
(b) 28.36 MHz (c) 63.87 MHz
(d) 21.39 MHz
(e) Cannot be determined from this info.
Answer: (c). fLarmor = 42.58 Bz = 42.58 MHz/T × 1.5 T
= 63.87 MHz
Ref: “Medical Imaging: Essentials for Physicians”, A.B. Wolbarst, P. Capasso,
and A. Wyant. Wiley-Blackwell (2013), p. 314. (MPP booth)
![Page 30: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/30.jpg)
Transmitter H2O
principal principal Antenna
Power meter
Antenna
magnet
z
NMR Gedanken-Experiment on Water, 1T
monochromatic RF power absorption at (and only at) fLarmor, H O
sweep the RF f
Det
ecte
d
RF
pow
er
Transmitter f (MHz)
Resonance at 1T: 42.58 MHz
2
1T
![Page 31: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/31.jpg)
I-2. If the field homogeneity of a 1.5 T
scanner is measured to be one part per
million (1 ppm), what will be the
approximate spread in resonant
frequencies?
60%
11%
8%
6%
16% a. 1.5 Hz
b. 42.58 MHz
c. 42.58 kHz
d. 63.87 MHz
e. 63.87 Hz
![Page 32: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/32.jpg)
SAMs Q: I-2. If the field homogeneity of a 1.5 T scanner is measured to be
one part per million (ppm), what will be the approximate spread in
resonant frequencies?
(a) 1.5 Hz
(b) 42.58 MHz
(c) 42.58 kHz
(d) 63.87 MHz
(e) 63.87 Hz
Answer: (e). ΔfLarmor = (42.58×106 MHz/T) × (1.5 T) × (10 6)
= 63.87 Hz
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 319.
![Page 33: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/33.jpg)
Proton-Density (PD) MRI in the 1D patient
![Page 34: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/34.jpg)
Gradient magnet
–10 0 cm +10 cm
1.002 T
1.000 T
Bz(x)
0.998 T
x
x = [Bz(x) − B0] / Gx
z
1D Phantom in Principal B0 and Gradient Gx
Principal magnet Principal magnet
(1.002T 0.998T) / 0.20m = 20 mT/m
Gx ≡ dBz(x)/dx
B0
Bz(x) B0 = Gx× x
x
![Page 35: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/35.jpg)
x
–10 0 cm +10 cm 2. 3.
1.002 T
1.000 T
B(x)
0.998 T x
Gx x = [Bz(x) − B0] / Gx
sweep the RF f
z
42.58 1. f (x)
42.62 MHz
1D PD-MRI: fLarmor = fLarmor[Bz(x)]
PD MR Image
4.
0.
Bz(x) = fLarmor / 42.58
3. 4. x
![Page 36: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/36.jpg)
42.62 MHz 42.58
Pixel Brightness, PD Voxel Position, x
Amplitude of
NMR Peak, A( f )
fLarmor of
NMR Peak
Bz (x) PD(x)
A( f )
0 +5 10 cm
MRI
x
Summary: PD MRI on 1D Patient
1.
2.
3. 4'.
4.
![Page 37: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/37.jpg)
Proton-Density MRI contrast from differences in PD
![Page 38: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/38.jpg)
respiration aortic pulsation
Two MRI Motion Artifacts
![Page 39: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/39.jpg)
I-3. The net magnetic field Bz(x) is
measured to be 0.999 T at
x = 0.05 m and 1.001 T at +5 cm.
What is Gx?
5%
13%
38%
29%
15% a. 0.01 T/m
b. 0.02 T/m
c. 20 mT/m
d. 0.2 T/cm
e. 0.2 T/m
![Page 40: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/40.jpg)
SAMs Q: I-3. The net magnetic field Bz(x) is measured to be 0.999 T at
x = 0.05 m and 1.001 T at +5 cm. What is Gx?
(a) 0.01 T/m
(b) 0.02 T/m
(c) 20 mT/m
(d) 0.2 T/cm
(e) 0.2 T/m
Answer: (c). 20 mT/m. ΔBz(x) / Δx = 2 mT / 0.1 m
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 318.
![Page 41: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/41.jpg)
44
Part 2:
Magnetization
& Relaxation
Net magnetization, m(x,t), of the voxel at x
T1 Spin-Relaxation of m(x,t),
T1 MRI of the 1D Patient
Sketch of the MRI Device
![Page 42: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/42.jpg)
Net magnetization, m(x,t), of the voxel at x
![Page 43: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/43.jpg)
Net Magnetization, m(x,t), for the Single Voxel at Position x: magnetic field from the ensemble of protons or needles themselves
Single voxel at position x
Gentle agitation (noise energy)
m(x,t) Bz > 0
![Page 44: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/44.jpg)
i) What is the magnitude of voxel magnetization
at dynamic thermal equilibrium, m0?
ii) How long does it take to get there (T1)?
iii) What is the mechanism?
Voxel’s MRI Signal Proportional to Its Magnetization, m(x,t)
![Page 45: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/45.jpg)
Switching Bz(x) On at t = 0 Induces Magnetization m(x,t) from protons in voxel at x
m(x) = 0
m(x,t) Bz > 0
t = 0
t >> 0
voxel at x
Bz(x) = 0
![Page 46: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/46.jpg)
Shaking (Noise) Energy:
too much too little just right
Filling Four Energy Levels of Marbles vs. Noise Level equilibrium from battle between energy and entropy
(all slippery; black balls denser)
![Page 47: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/47.jpg)
0
~ 0
N μz
5×10– 6 N μz
0 tesla
0.01 T or
t = 0+*
»1.5 T
1.5 T
t >> 0
m0 Bz
* after abruptly turning on Bz , or after a 90º pulse.
Magnetization in Voxel at x, under Dynamic Equilibrium: m0(x,t) = [N–(x,t) – N+(x,t)]×μ , t → ∞
collective magnetic field produced by all the protons in it (Boltzmann)
μ
![Page 48: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/48.jpg)
|m0(x)| and Signal from it Increase with B0
p.s., trade-off: SNR, resolution, acquisition-time
1.5 T 7 T (+Gd)
![Page 49: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/49.jpg)
T1 Spin-Relaxation of m(x,t)
![Page 50: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/50.jpg)
Voxel’s MRI Signal Proportional to Its Magnetization, m(x,t)
i) What is the magnitude of voxel magnetization
at thermal equilibrium, m0?
ii) How long does it take to get there (T1)?
iii) What is the mechanism?
![Page 51: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/51.jpg)
t = 0 ms t = 1 ms t = 2 ms
m = 0 m = 2μ m = 4μ
Disturbed System Moving toward Up-Down Equilibrium energy imparted to individual ‘down’ spins from ‘outside’
spin ‘tickled’ down by fLarmor component of magnetic noise;
emits RF photon, phonon. a few can be kicked ‘up’, as well.
m(0)
m(1)
m(2)
![Page 52: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/52.jpg)
6 12 18 hr
0
Decay of Tc-99m Sample to Final Value, n(∞) = 0
n(0) radionuclei at initially
n(t) remaining after time t.
n(∞) at ‘equilibrium’ n(∞) = 0
dn/dt(t) = λ n(t)
1 n(t)
n(0)
n(∞)
dn/dt ~ [n(t) n(∞)]
n(t) = n(0) e λt
½
scint. decay (t) pop. growth (t) photon atten. (x)
tracer conc. (t) cell killing (D) ultrasound atten. (x)
![Page 53: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/53.jpg)
[m0 – mz(t)]
mz(
t)
250 500 750 ms t 0
Return of Voxel’s mz(t) to Final Value, mz(∞) ≡ m0
rate
d [m0 – mz(t)] / dt = (1/T1) [m0 – mz(t)]
mz(t)/m0 = 1 e t / T1
Actually, dynamic equilibrium more complicated: Spins tickled down and up!
mz(∞) ≡ m0
![Page 54: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/54.jpg)
T1 MRI of the 1D Patient
![Page 55: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/55.jpg)
–10 0 cm +10
0.998 1.000 1.002 T
RF transmit
RF receive,
FT
CSF lipid
f (x)
42.62 42.58
PD(x)
T1 for 2 Voxels: Lipid vs. CSF both at fLarmor of H2O for local field
![Page 56: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/56.jpg)
0 5 cm
t = 0+
t = TR1
t = TR2
t = TR3
1. First, do lipid at x = 0.
2. Strong burst of RF over range
42.58 MHz ± 250 Hz causes
N– ~ N+
3. After TR1 delay, sweep through
fLarmor , record peak’s amplitude.
4. Repeat for several other TRi values.
5. Plot.
Recovery of mz(t) over Time, from mz(TRi) Measurements
longitudinal component of net voxel magnetization, mz(t)
![Page 57: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/57.jpg)
mz(
t)/m
0
250 500 750
1
TR2
TR3
TR1
TR4 0.63
tread (ms) 0
mz(TR)/m0 = (1 − e − TR / T1)
curve-fit for set of {TRi} for voxel at x = 0
T1
T1
lipid: T1 ~ 250 ms
T1 MR image
by convention for T1-imaging: pixel white for fast-T1 tissue
Spritely Brightly
![Page 58: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/58.jpg)
mz(x,t)/m0(x) = (1 − e− t / T1(x)) repeat for CSF voxel at x = 5 cm, fLarmor = 42.62 MHz…
T1
lipid: ~ 250 ms
CSF: ~ 2,000 ms
T1 MR image
CSF: T1 = 2,000 ms
x = +5 cm
Lipid: T1 = 250 ms
x = 0
t
mz(
t) /
m0
![Page 59: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/59.jpg)
Gd
sub-cut. fat
T1 ~ 260 ms
CSF
T1 ~ 2000 ms
T1-w MR Image
![Page 60: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/60.jpg)
Tissue PD T1, 1 T T1, 1.5 T T1, 3 T T2 p+/mm3, rel. (ms) (ms) (ms) (ms)
pure H20 1 4000 4000 4000
brain CSF 0.95 2000 2000 2000 200
white matter 0.6 700 800 850 90
gray matter 0.7 800 900 1300 100
edema 1100 110
glioma 930 1000 110
liver 500 40
hepatoma 1100 85
muscle 0.9 700 900 1800 45
adipose 0.95 240 260 60
Approximate Relaxation Times of Various Tissues
![Page 61: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/61.jpg)
Voxel’s MRI Signal Proportional to Its Magnetization, m(x,t)
i) What is the magnitude of voxel magnetization
at thermal equilibrium, m0?
ii) How long does it take to get there (T1)?
iii) What is the mechanism?
![Page 62: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/62.jpg)
65
In MRI, the only thing a proton
is ever aware of, or reacts to, is the
local magnetic field, Blocal(t).
!!!
But the source of fLarmor(Blocal(t)) can be either
external (BRF) or internal (e.g., moving partner)
!!!!!
![Page 63: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/63.jpg)
Random BRF(t) at fLarmor Causes T1-Transitions
☻ ☻
variations in proton magnetic dipole-dipole interactions
1.5 Å
O
H H
O
H
H
4×10 – 4 T
each water proton produces magnetic field fluctuations
of various frequencies, including local fLarmor , at its partner proton
![Page 64: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/64.jpg)
Restrictions on Rotations of Water Molecules
more or less hydration free
bound layer
![Page 65: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/65.jpg)
Rotational Power Spectra, J( f ), of Water for several water populations
Water on small molecule
Pro
bab
ilit
y /
rel
ativ
e num
ber
fLarmor
T1 spin flips
Pure water
Water on large biomolecule
Magnetic noise (water tumbling, etc.) frequency
Slow motion Rapid
![Page 66: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/66.jpg)
Water on intermediate
sized molecule
Pure water
Rel
axat
ion T
ime,
T1
1.5 T fLarmor
T1
Water on large, slow biomolecule
Magnetic noise (water tumbling, etc.) frequency
Slow motions Rapid
Average Water T1 Determined by Noise Power Spectrum,
J( fLarmor)
![Page 67: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/67.jpg)
MRI:
Water, Lipids of Soft Tissues
their Hydrogen Nuclei.
Spin-Relaxation Times (T1, T2)
their Spatial Distributions!
![Page 68: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/68.jpg)
Sketch of the MRI Device
![Page 69: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/69.jpg)
72
Damadian’s Indominable, 1977 (Smithsonian)
Nobel Prize, 2003 Paul Lauterbur
Peter Mansfield
![Page 70: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/70.jpg)
BRF RF
MIX DAC
Operator console
Gx
ADC
B0
RF
fringe fields
partially shielded
y
z
x
PACS
Major Components of a Superconducting MRI System
![Page 71: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/71.jpg)
z
x
y B0
MRI Magnets
Open (most of this presentation)
electromagnetic or permanent
Superconducting
B0 z
e.g., niobium-titanium wire
B0 : < 0.5T, 1.5 T, 3.0 T, (7 T)
Homogeneity: <10 ppm
Shielding: passive and active
Cryogen: 0.1 liter He / y
Weight: 4 tons (supercond.)
![Page 72: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/72.jpg)
BRF
z
x
Gz ≡ B0
Gx ≡ ΔBz(x)/Δ x
Three External Magnetic Fields in Open Magnet MRI B0 , Gz , and Gx all point along z!
ΔBz(z) /Δ z
![Page 73: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/73.jpg)
B0 z
x-Gradient dBz /dx 20 − 60 mT/ m
Rise time 0.3 ms (to reach 10 mT/ m)
Slew rate 50 − 200 mT/m/ms
x-Gradient Magnet Winding for Superconducting Magnet
one layer of x-gradient coil
![Page 74: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/74.jpg)
77
Artifact: Gradient Non-Linearity
![Page 75: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/75.jpg)
II-4 Gradient coils affect the strength of
the magnetic field that, at all locations in
space, point…:
a. along the x direction of the scanner
b. along the y direction of the scanner
c. along the z direction of the scanner
d. along all directions of the scanner not enough information given here to answer a. b. c. d.
5%
52%
40%
3%
![Page 76: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/76.jpg)
SAMs Q: II-4 Gradient coils affect the strength of the magnetic field that, at
all locations in space, point…:
(a) along the x direction of the scanner
(b) along the y direction of the scanner
(c) along the z direction of the scanner
(d) along all directions of the scanner
(e ) not enough information given here to answer
Answer: (c). Along the principal magnetic field, B0, hence the
z-axis
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 316.
![Page 77: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/77.jpg)
RF Coils
BRF : 20 μT
Pulse on-time: 3 msec
RF power: 15 – 25 kW
SAR: 2 – 20 W/ kg
![Page 78: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/78.jpg)
‘Parallel’ RF Receiving Coils for Much Faster Imaging transmit coils coming
![Page 79: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/79.jpg)
II-5 The acronym used to describe the
amount of RF radiation uptake in patient
tissue is:
2%
3%
1%
90%
4% a. REM
b. SAR
c. CTDI
d. STIR
e. RARE
![Page 80: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/80.jpg)
SAMs Q: II-5. The acronym used to describe the amount of RF radiation
uptake in patient tissue is:
(a) REM
(b) SAR
(c) CTDI
(d) STIR
(e) RARE
Answer: (b). Specific Absorption Rate
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 349.
![Page 81: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/81.jpg)
Part 3:
“Classical” MRI
‘Classical’ Approach to NMR
FID Image Reconstruction, k-Space
T1W MRI
![Page 82: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/82.jpg)
Normal modes, resonance, precession, nutation
Free Induction Decay (FID) in a voxel, without the decay
e.g., very slow T1 relaxation
Untangling the FID RF signals from a row of voxels:
Temporal Fourier Series approach
FID imaging of the two-voxel 1D patient
FID Imaging via k-Space; Spatial FT
‘Classical’ Approach to NMR;
FID Image Reconstruction, k-Space
![Page 83: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/83.jpg)
quantum state function
| ψ
Simple QM Classical Bloch Eqs.
|↑ , |↓
transitions between precession, nutation of spin-up, spin-down states voxel magnetization, m(t)
fLarmor , m0 , T1 fLarmor , T2 , k-space oversimplified exact; from full QM
The Two Approaches to NMR/MRI (incompatible!)
for expectation values
now this
![Page 84: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/84.jpg)
Normal Modes, Resonance, Precession, Nutation
![Page 85: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/85.jpg)
Normal Mode, at fnormal
fnormal
fnormal
fnormal
![Page 86: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/86.jpg)
A Normal Mode of a 2-D Pendulum
fnormal
![Page 87: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/87.jpg)
Normal Mode Precession about External Gravitational Field
J(t): Angular Momentum
With torque, τ:
dJ / dt = τ
Equation of Motion
Angular acceleration is just like
dp / dt = F
but here, J(t) changes direction only:
Precession at
r
mg
fprecession
τ τ
J(t)
fnormal
![Page 88: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/88.jpg)
x
mz(t) longitudinal magnetization
z
transverse magnetization
mxy(t) = [mx(t) + my(t)]
Normal Mode Precession of Voxel m(x,t) in Magnetic Field can be derived rigorously from quantum mechanics
Bz(x)
fnormal = fLarmor(x)
m(t) = [mx(t) + my(t) + mz (t)]
y
![Page 89: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/89.jpg)
Equation of motion for spinning body
d J /dt = τ (external torque)
d( μ / γ) / dt = τ
Lorentz torque on spins at x with magnetic moment μ in Bz(x):
τ = μ×Bz(x)
Equation of motion becomes:
d μ(x,t) /dt = γ μ(x,t)×Bz(x) .
Sum/average over all protons in voxel:
d m(x,t) /dt = γ m(x,t) ×Bz(x) With T1 relaxation along z-axis:
d m(x,t) /dt = γ m(x,t) ×Bz(x) + [ m(x,t) m0(x)]ẑ / T1
Classical Bloch Equations of Motion for m(x,t) in B0
Expectation Value,
m(x,t) , behaves classically
(vector cross product)
recall: μ = γ J
![Page 90: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/90.jpg)
Precession of m(x,t) about B0 at fLarmor = (γ / 2π) Bz(x)
as seen from a frame that is
x'
z'
y'
m(x,t)
The ponies don’t advance when you’re on the carousel; It’s as if B0 = 0 !
x
y
as if B0 = 0
Fixed Rotating at fLarmor(x)
m(x,t)
z
![Page 91: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/91.jpg)
Resonance Energy Transfer when fdriving = fnormal
Fres
Fres Fres
![Page 92: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/92.jpg)
Normal Mode and Resonance of a 2-D Pendulum
fnormal
fdriving = fnormal
Nutation Precession
![Page 93: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/93.jpg)
string
Cone of Precession
Nutation at Resonance
And Now for Something Completely Different: Nutation
![Page 94: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/94.jpg)
fLarmor =
(γ/2π) B0
y
x
m
m z
BRF
Bz(x)
fNutation =
(γ/2π) BRF
precesses at fLar = (γ /2π) Bz(x)
nutates at fnut = (γ /2π) BRF
(always!)
(only when BRF is on!)
Nutation of the Voxel’s Magnetization, m(x,t) BRF /B0 ~ 10 5 10 4
![Page 95: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/95.jpg)
Free Induction Decay (FID) in a voxel, without the decay e.g., very slow T1 relaxation
![Page 96: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/96.jpg)
Tissue
RF
m(x,t) for a Single Voxel at x and Precessing in the x-y Plane following a 90º pulse
RF
mxy(x,t)
RF transmit coil
RF detect. coil
(Faraday)
![Page 97: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/97.jpg)
Fouri
er
com
ponen
t
42.58 MHz
t (µs)
FID Precession, Reception, Fourier Analysis (single voxel)
n.b. measure induced V(t), not power absorption (as before)
F
m(t) x
y
MR
si
gnal
x = 0 cm
antenna
f (MHz)
![Page 98: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/98.jpg)
In MRI, the only signal
you ever see comes from
the set {m(x,t)}
all precessing in the x-y plane
!!!
![Page 99: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/99.jpg)
III-6. The rate of magnetization nutation
depends upon:
a. the magnitude of the magnetization, |m(t)|
b. the strength of the principal magnetic field, |B0|
c. strength of the x-gradient field, |x × Gx|
d. the strength of the RF magnetic field, |BRF(t)|
e. T1 a. b. c. d. e.
8%12%
3%
69%
8%
![Page 100: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/100.jpg)
SAMs Q: III-6. The rate of magnetization nutation depends upon:
a) the magnitude of the magnetization, |m(t)|
b) the strength of the principal magnetic field, |B0| c) strength of the x-gradient field, |x × Gx|
d) the strength of the RF magnetic field, |BRF(t)| e) T1
Answer: (d).
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 328.
![Page 101: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/101.jpg)
Untangling the FID RF Signal from Two Voxels:
temporal Fourier series approach
![Page 102: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/102.jpg)
positive (in-phase)
interference
Wave Interference in Time or Space
negative interference
![Page 103: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/103.jpg)
decomposition
Fouri
er
com
ponen
ts
f (Hz)
k (cm1)
t (sec)
x (cm)
interference
time or
space C
om
posi
te
bea
t si
gn
al
Sep
arat
e si
gnal
s
Wave Interference and Spectral Analysis
via Fourier analysis, F
![Page 104: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/104.jpg)
0
0 1f1 3f1 5f1 7f1
Com
ponen
t am
pli
tude
f
f
2
2 /3π
2 /5π
t
½
S(t)
Components
1st harmonic fundamental
3rd harmonic
5th
F
Fourier Decomposition of Periodic Temporal Signal
Hz
0 f1 f3 f5 f7
f1
f3
f5
S(t) ~ ½ + (2/π){sin (2π f1t) + ⅓ sin (6π f1t) + 1/5 sin (10π f1t) + …}
2 /π
f
fundamental: f1 Hz (cycles/sec)
1/f1
spectrum orthonormal
basis vectors
(2 /7π)
![Page 105: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/105.jpg)
FID imaging of the two-voxel 1D patient
![Page 106: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/106.jpg)
BRF
RF receive
e.g., FID from 2 water slices, at x = 0 and 5 cm; little decay!
–10 0 cm 5 +10 x
1.002 T
1.000 T
0.998 T 42.58 42.62 MHz
B(x)
RF transmit
fLarmor(x) = (γ/2π) (x×Gx) (in rotating frame)
![Page 107: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/107.jpg)
Gx
t
90º
puls
e
t
PD
(x)
10 5 0 5 10 cm
x
water ½ water
z
B0
y
x
while gradient is on…
FID Following Wide-Bandwidth 90° RF Pulse covers fLarmor(x) for all N voxels while Gx is being applied!
* *
* *
![Page 108: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/108.jpg)
Volt
ages
Separate
RF signals (μs)
n.b.: m(x,t) = m(x,0)e– 2πi f (x) t FID: After Wide-Band RF 90º Pulse Centered on fLarmor(B0)
mxy(x=0) y mxy(x=5)
(μs)
Fo
uri
er
spec
tru
m
(MHz)
FID PD MRI
Detected FID signal
F
S(t
)
x = fL(x) / (γ/2π) Gx
Temporal
x
z
![Page 109: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/109.jpg)
A(
f )
R(x
)
f
x
S(t
)
t
Signal spectrum MRI signal
Real-space representations
To Summarize What We Have Done So Far with FID follow temporal with isomorphism of A( f ) to real-space, R(x)
42.58 MHz 42.62
0 cm +5
F
x = 2π f (x) / γGx
t ↔ f
A( f ) = S(t) e– 2πi f (t) t dt
F
![Page 110: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/110.jpg)
FID Imaging via k-Space; Spatial FT
![Page 111: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/111.jpg)
A(
f )
f
S(t
)
t
Signal spectrum Detected FID signal
Real-space representation
42.58 MHz 42.62 sec
R(x
) x
0 +5 cm
Temporal: t ↔ f
x = 2π fLarmor(x) / γ Gx
Again, What We Have Done So Far:
F
![Page 112: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/112.jpg)
0
2/π
2/3π
2/5π
½
Co
mp
onen
t am
pli
tud
e F
x
1/k1 S(x)
fundamental: k1 (cycles / mm)
S(x) ~ ½ + (2/π) [sin (2π k1 x)
+ ⅓ sin (6π k1 x) + 1/5 sin (10π k1 x) + … ]
kx
k1 3k1 5k1 7k1 …
Now Consider 1D Spatial Fourier Analysis
1
0 k1 k3 k5 k7 …
![Page 113: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/113.jpg)
A(
f )
f
S(t
)
t
Signal spectrum
42.58 MHz 42.62
α(k
)
k
sec
k-space representation
Experiment: Continue on with a FT from x- to kx-Space
R(x
) x
0 +5 cm
Spatial: kx ↔ x
Temporal: t ↔ f
α(k) = R(x) e–2πi kx x dx
Real-space representation
x = 2π fLarmor(x) / γ Gx
F
F
Detected FID signal
![Page 114: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/114.jpg)
A(
f )
f
S(t
)
t
Signal spectrum
Real-space representation
42.58 MHz 42.62
α(k
)
k
sec
R(x
) x
0 +5 cm
x = 2π fLarmor(x) / γ Gx
Temporal: t ↔ f
F
And Complete the Loop Linking t-, f-, x- and kx-Spaces
k-space representation
kx(t) ≡ γ Gx t /2π
Spatial: kx ↔ x
F
Detected FID signal
![Page 115: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/115.jpg)
A(
f )
f
S(t
)
t
Signal spectrum
Real-space representation
42.58 MHz 42.62 sec
R(x
) x
0 +5 cm
kx(t) ≡ γ Gx t /2π
So, We Can Get from S(t) to R(x) in Either of Two Ways! but only the approach via k-space works in 2D and 3D
x = 2π fLarmor(x) / γ Gx
F
F 1
fLarmor(x) t = kx(t) x
Detected FID signal
α(k
)
k
k-space representation
![Page 116: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/116.jpg)
kx
R(x) = α(k) e+2πi kx dk
k-Space Procedure for FID in 1D Phantom
S(t) comprised of contributions from the m(x) for all x
m(x) = S(t) e+2πi k(t)·x d 3k
m(x,t) = m(x,0)e– 2πi f (x) t = m(x,0) e– 2πi kx(t) x
S(t) = S(k(t)) ~ m(x) e–2πi kx(t)
x dx .
Therefore, taking the inverse FT, F :
S(t
)
α(k
)
t
kx(t) ≡ γ Gx t /2π
k
Real-space representation
R(x
) x
0 +5 cm
k-space representation
Detected FID signal
F 1
1
![Page 117: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/117.jpg)
Spatial Waves, and Points in k-Space
![Page 118: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/118.jpg)
Point in k-Space and Its Associated Wave in Real Space
k-Space
k-Space
kx
ky
![Page 119: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/119.jpg)
Points in k-Space and Their Waves in Real Space
k-Space
kx
ky
![Page 120: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/120.jpg)
+ =
Composite Patterns in k-Space and Real Space linearity
![Page 121: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/121.jpg)
k-Space Real Space
kx
ky
x
F
y
Fourier Transform of k-Space Pattern to Real Space
![Page 122: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/122.jpg)
Fourier Transform of MRI Data in k-Space to Real Space
F
![Page 123: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/123.jpg)
F
Fourier Transform from Parts of k-Space to Real Space
![Page 124: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/124.jpg)
Herringbone Artifact noise spike during data acquisition
Zhou/Gullapalli
![Page 125: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/125.jpg)
III-7 Information about the structural detail
in an image is:
a. dependent on the Fourier transform.
b. contained in the periphery of k-space.
c. blurred by increasing separation of lines in k-space.
d. contained in the center of k-space.
e. related to gradient duration.
a. b. c. d. e.
7%
60%
2%
28%
3%
![Page 126: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/126.jpg)
SAMs Q: III-7 Information about the structural detail in an image is:
a) dependent on the Fourier transform.
b) contained in the periphery of k-space.
c) blurred by increasing separation of lines in k-space.
d) contained in the center of k-space.
e) related to gradient duration.
Answer: (b).
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 337.
![Page 127: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/127.jpg)
Part 4:
Spin-Warp; 2D
Spin-Echo Reconstruction (SE vs. FID)
T2 Spin-Relaxation (Static vs. Random Dephasing)
T1-w, T2-w, and PD-w S-E MR Imaging
Spin-Echo / Spin-Warp in 2D (2X2 illustration)
![Page 128: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/128.jpg)
Spin-Echo Reconstruction
Spin Echo vs. FID
![Page 129: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/129.jpg)
t
mxy
(x,t
) /
mxy
(x,0
)
Static Field de-P hasing of FID
in x-y Plane of Spins in Each Voxel SFd-P from static-field inhomogeneities & susceptibility effects
This de-phasing is REVERSABLE!!!!
Rate of SFd-P decay:
1/ TSFd-P = κ ΔB0 + κ' Δχ
0
1
mxy(x,t)
mxy(x,t) e– t / T SFd-P ~
t=0
n.b., mxy(x,t)….
but still 1D phantom!
FID
Δ fLarmor ~ ΔB0
![Page 130: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/130.jpg)
i
ii
iii
Kentucky Turtle-Teleportation Derby Illustration of Spin-Echo
t = 0
t = ½ TE
t = TE
iv
v
![Page 131: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/131.jpg)
x
y
t = 0
t = ½ TE
t = TE
m(x,t)
Spin-Echo Generates an Echo and Eliminates Effects of SFd-P
(a)
(b)
(c)
(d)
(e)
Local magnetic environment
for each spin packet is static.
So this de-phasing can be
REVERSED!!!
180º
90º
T2 dephasing, by contrast,
is random over time,
and can NOT be un-done!!
![Page 132: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/132.jpg)
RF
pu
lse
S(t) Echo
S-E Sequence Using 180º RF Pulse and Readout Gradient with 256 voxels, e.g., sample/digitize echo signal 256-512 times
readout
Gx fLarmor(B0 ± Gx × ½ FOV)
90º 180º
t
t
t
![Page 133: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/133.jpg)
R(x
) 0 cm 5
t
S(t
)
x
kx
α(k
)
k-space representation α(k): Amplitude and phase of spatial
frequency (k) Real-space representation
Sampled SE signal
R(x) = α(k) e+ikx dk
k-Space (spatial frequency) Procedure for SE in 1D Phantom
kx → x
kx = (γ/2π) Gx t
S(t) made up of contributions from m(x) for all x;
m(x) can be extracted from S(t) with kx → x F :
m(x) = S(t) e 2πi k(t)·x d 3k
S(t) = S(k(t)) ~ m(x) e– 2πi kx(t) x dx
F –1
![Page 134: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/134.jpg)
S(t) = S(k(t)) ~ m(x) e– 2πi kx(t) x dx .
kx (t) for all voxels increases linearly with t while the echo signal is being received and read. With signal sampled at 512 adjacent instances spaced ∆t apart, t represents the exact sampling time: the nth sample is taken a time tn = n × ∆t after Gx was turned on. Different values of k correspond to different sampling times. In particular, for tn , kn = [Gx γ / 2π] tn
Larger k-values correspond to greater spatial frequencies!
During Readout, kx Increases Linearly with t
141
![Page 135: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/135.jpg)
k = kmax kmax
tn
k = 0
S-E reads out from kn= kmax to k = 0 to k = kmax
During Readout, kx Increases Linearly with t
Signal is sampled sequentially at 256-512 times spaced ∆t apart;
tn is the exact sampling time after Gx is turned on.
k(t) for all voxels increases linearly with t while the echo signal is
being received and read: kn = [Gx γ / 2π] tn. Later sampling times
(and larger k-values) correspond to greater spatial frequencies.
t512
![Page 136: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/136.jpg)
T2 Spin-Relaxation
T2 Relaxation refers to the rate at which the transverse
magnetization decays (disappears).
T2 relaxation results from T1-Events and
Non-Static, Random, Non-Reversible
Proton-Proton Dipole Interactions
Both Contribute to the decay rate (1/T2)
(Specifically, any process that either reduces the number of transverse spins
or their relative phase relationship will add to T2 relaxation.)
![Page 137: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/137.jpg)
Spin Multi-Echo:
we might expect
mxy(x,t) ~ e– t /
T2
However, Harsh Reality
Thus, the Spin-Echo Signal Intensity S(t) Does Decay,
and decays much Faster than 1/T1!
S(t)
RF t
90º 180 180º 180º 180º
! ! ! ! !
Spin-Echo Spin De-Phasing Is Caused by T1 Events as well as
By Random, Proton-Proton Dipole Interactions
![Page 138: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/138.jpg)
Spin-Spin (Secular) De-Phasing in Bound Water with its protons precessing in the x-y plane
O
H
H
C
Quasi-static spin-spin interactions does not involve exchange of energy like T1 relaxation!
C
H
H
H
B C
H
![Page 139: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/139.jpg)
1
mxy
(t)
/ m
xy(0
)
20 40 60 ms t 0
Exponential T2-Caused De-Phasing of mxy(t) in x-y Plane
dmxy (t) / dt = (1/T2) mxy (t)
dm(x,t)/dt = γ m(x,t)×Bz(x) [m(x,t) m0(x)] ẑ [mx x + my ŷ]
classical Bloch Equation T1 T2
rate
mxy (t) /mxy(0) = e t / T2
![Page 140: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/140.jpg)
(TSFd–P)
One Last Member of the Spin-Relaxation Family Tree: T2*
spin-echo
T1
FID, Gradient-Echo fastest T2*
T2
T1
G-E generally much
faster than S-E T2
Discrete spin-dephasing: involves Δ E
Continuous spin-dephasing: no Δ E!
![Page 141: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/141.jpg)
T2 relaxation refers to:
3%
72%
7%
11%
7%a. The rate at which longitudinal
magnetization recovers.
b. The rate at which longitudinal
magnetization disappears.
c. The rate at which transverse
magnetization recovers.
d. The rate at which transverse
magnetization disappears.
e. The rate at which tissue is
magnetized.
![Page 142: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/142.jpg)
T2 relaxation refers to:
a) the rate at which longitudinal magnetization recovers.
b) the rate at which longitudinal magnetization disappears.
c) the rate at which transverse magnetization recovers.
d) the rate at which transverse magnetization disappears.
e) the rate at which tissue is magnetized.
Answer: (d).
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 364.
![Page 143: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/143.jpg)
Tissue Contrast Weighting (w) in S-E MRI
T1-w, T2-w, and PD-w
![Page 144: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/144.jpg)
Tissue PD T1, 1 T T1, 1.5 T T1, 3 T T2 p+/mm3, rel. (ms) (ms) (ms) (ms)
pure H20 1 4000 4000 4000
brain CSF 0.95 2500 2500 2500 200
white matter 0.6 700 800 850 90
gray matter 0.7 800 900 1300 100
edema 1100 110
glioma 930 1000 110
liver 500 40
hepatoma 1100 85
muscle 0.9 700 900 1800 45
adipose 0.95 240 260 60
Relaxation Rates: 1/T2 ~ 10 × (1/ T1) Typical T1 and T2 Relaxation Times
![Page 145: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/145.jpg)
Three Different Forms of MRI Contrast created by, and reflecting, three quite different physical properties
T1 T2 PD
![Page 146: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/146.jpg)
Gx
readout
i ii
Multiple Spin-Echo Pulse Sequence
RF 90º 180º 90º 180º
![Page 147: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/147.jpg)
MRI Signal Strength at t = TE Depends on….
Inherent Parameters Operator Settings
T1 TR
T2 TE
PD
time since previous
S-E sequence
S(t = TE) ~ PD (1 e−TR / T1 ) e−TE / T2
current dephasing
in x-y plane
prior regrowth
along z-axis
proton density
bright regions:
mxy large at t = TE
![Page 148: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/148.jpg)
In a spin-echo pulse sequence, a
short TE will:
2%
2%
1%
83%
13% a. Minimize T1 image contrast
b. Eliminate T2 effects
c. Result in a lower SNR
d. Increase the effects of static-field de-phasing
e. Enhance tissue susceptibility differences
![Page 149: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/149.jpg)
(a) Minimize T1 image contrast
(b) Eliminate T2 effects
(c ) Result in a lower SNR
(d) Increase the effects of static-field dephasing
(e) Enhance tissue susceptibility differences
Answer: (b).
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 368.
In a spin-echo pulse sequence, a
short TE will:
![Page 150: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/150.jpg)
current de-phasing
in x-y plane
prior regrowth
along z-axis
proton density
S(t~TE) ~ PD (1 e−TR / T1 ) e−TE / T2
Short TE to minimize T2 impact
TR ~ T1av to maximize
contrast
lipid CSF
Short-T1 tissues bright
(sprightly brightly)
T1-w
T1-weighted – Short TE to Eliminate T2 Contribution
T1short
![Page 151: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/151.jpg)
TR
180° TE 90° 90° 90°
mxy(TE)
CSF
500 ms
20 ms
mz(t)
lipid
i ii
mz(TR)
m0
TR
CSF
TR TR
T1-w – Short TE to Eliminate T2 Contribution
TE Short (20 ms);
TR ~ T1av (500 ms)
time
lipid
lipid CSF
Short T1
Bright
lipid
CSF
![Page 152: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/152.jpg)
current de-phasing
in x-y plane
prior regrowth
along z-axis
proton density
S(t~TE) ~ PD (1 e−TR / T1 ) e−TE / T2
For T2-w imaging
lipid CSF T2-w
Long TR: eliminate T1 impact
TE at mid-T2: maximize contrast
Long-T2 tissues bright
T2-w – Long TR to Eliminate T1 Contribution
T2 long
![Page 153: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/153.jpg)
TR
90° TE
Mxy(t)
90°
CSF
2000 ms
~ 80-100 ms
Mz(t)
time
i ii TR TR
T2-w – Long TR to Eliminate T1 Contribution TE ~ mid-T2 to maximize T2 contrast
CSF
lipid
180° TE
lipid Mxy(TE)
Mxy(TR+)
TE Long (80 ms);
TR Long (2000 ms)
![Page 154: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/154.jpg)
T1-w T2-w PD-w
PD-, T1-, & T2-Weighted Spin-Echo Images (1.5T)
TR mid- (~T1av) long long (ms) 300 − 700 1,500 − 3,500 1,500 − 3,500 TE short mid- (~T2av) short (ms) 0 − 25 60 − 150 10 − 25 Bright short T1 long T2 high PD
SNR good lower best
![Page 155: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/155.jpg)
Which of the following would appear bright
on a T2-weighted image of the brain?
0%
6%
0%
7%
87% a. CSF
b. Fat
c. Bone
d. White Matter
e. Air
![Page 156: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/156.jpg)
Which of the following would appear bright on a
T2-weighted image of the brain?
(a) CSF
(b) Fat
(c) Bone
(d) White matter
(e) Air
Answer: (a) cerebral spinal fluid.
Ref: “Medical Imaging”, A.B. Wolbarst et al., Wiley-Blackwell (2013), p. 368.
![Page 157: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/157.jpg)
One of the earliest 2D imaging methods was
Sensitive Point Reconstruction.
This method used oscillating gradient fields to
produce a net field stable in only one voxel at a time.
That “sensitive point” was then scanned in space.
2D Images using Spin-Echo/Spin-Warp
![Page 158: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/158.jpg)
2 different superimpositions
3 components a
b
In 2-D MRI, phase is as important as frequency
and is used to add a second spatial dimension.
![Page 159: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/159.jpg)
x
y
z
m(1)
m(2)
m(3)
m(4)
Assume: PD Map of Thin-Slice 2D, 4-Voxel Patient after 90º pulse drives M(t) into x-y plane…
viewed from feet to head
1 3
2 4
PD Map
2D Spin-Warp 2X2 Matrix Illustration
Pixel #
![Page 160: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/160.jpg)
→π
second sequence
Gz
Gy
Gx
for S0 for Sπ
first sequence
TR TR
→0
180º phase difference
between rows
RF slice
selection
0º phase difference
between rows
Spin-Echo, Spin-Warp Sequence for 2×2 Matrix involves 2 spin-echo pulse sequences
phase encoding gradient
![Page 161: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/161.jpg)
S0(1,2,3,4) = 7 (e.g.)
1 3
2 4
After (Gy=0) phase encoding
receiver
S0(1,2,3,4)
fLarmor
1 3
1 3
2 4
1 3
Gx
Gy
during (Gx= 0) readout
7 = m(1) + m(2) + m(3) + m(4) [S0(1,2,3,4)] F
e.g., No x- or y-Gradients: Gy = Gx = 0
F
(Same Phase) (Same frequency)
![Page 162: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/162.jpg)
S0(3,4) = 2 S0(1,2) = 5
1 3
2 4
Gy = 0
receiver
1st S-E Sequence: x-Gradient Only, On During Readout
1 3
S0(1,2) + S0(3,4)
S0(3,4) = 2 = m(3) + m(4)
S0(1,2) = 5 = m(1) + m(2) [S0(1,2) + S0(3,4)]
F
F
1 3
2 4
Gx
(Same phase) (Different frequencies)
Gx≠ 0
5 2
![Page 163: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/163.jpg)
Sπ(1,2) = –3
φ + π
φ
Gy receiver
Sπ(1,2) + Sπ(3,4) Sπ(3,4) = 2
1 3
2 4
1 3
Sπ(1,2) = –3 = m(1) m(2) Sπ(1,2) + Sπ(3,4)
Sπ(3,4) = 2 = m(3) m(4)
F
First,
2nd S-E Sequence: y-Gradient, then x-Gradient
Gx
F
Gy → 180º Δ . Gx On During Readout
1 3
2 4
(Different phases) (Different frequencies)
Gy≠ 0 Gx≠ 0
+
-
+
+
-3 2
![Page 164: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/164.jpg)
S0(3,4) = 2 = m(3) + m(4)
S0(1,2) = 5 = m(1) + m(2) S0(1,2) + S0(3,4)
Sπ(1,2) = –3 = m(1) m(2) Sπ(1,2) + Sπ(3,4)
Sπ(3,4) = 2 = m(3) m(4)
4 Equations in 4 Unknowns
7 = m(1) + m(2) + m(3) + m(4) S0(1,2,3,4)
1 3
2 4
in phase: add
180º out of phase: subtract
F
F
F
Solution:
m(1) = 1
m(2) = 4
m(3) = 2
m(4) = 0
![Page 165: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/165.jpg)
90o pulse with Gz on selects
z-plane and initiates spin-echo
Free precession with Gy on
phase-encodes y-position
Gy(n) = n×Gy(1), n = 1, 2,…, 192
Reading NMR signal with Gx on
frequency-encodes x-position
Repeat, but with Gy(n+1) n = 1, 2,…, 192
Spin-Echo, Spin-Warp…. (256×192 matrix)
Gy 192×
Sample 512×
![Page 166: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/166.jpg)
Creation of an MRI ‘Image’ in 2D k-Space each line in k-space from data obtained during one Mxy(TE) readout;
different lines for different phase-encode gradient strength
Gphase # 96
Gphase #96
Gphase #1 Amplitude
frequency (kx)
![Page 167: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/167.jpg)
2D, 3D, 4D Imaging
Inversion Recovery (STIR and FLAIR)
Fast S-E; Gradient Recovery Imaging (GRE, e.g., EPI)
Dynamic Contrast-Agent Enhancement (DCE)
Magnetization Transfer
CNR and Other Quantitative Measures of Image Quality
Parallel-Coil Receive, Transmit; Shim Coils
Magnetic Resonance Angiography (MRA)
Perfusion Imaging
Diffusion Tensor Imaging (DTI)
Functional MRI (f MRI)
Image QA, and ACR Accreditation
MRI/PET, MRI-Elastography, MRI/DSA, MRI/US
Highly Mobile MRI (e.g., for strokes)
Zero-Quantum Imaging
Artificial Intelligence Diagnosis
MRI-Guided Radiation Therapy
Multiple Important MR Topics Not Addressed Here
![Page 168: A Brief Introduction to Magnetic Resonance Imagingamos3.aapm.org/abstracts/pdf/99-28903-359478-114743.pdfA Brief Introduction to Magnetic Resonance Imaging Anthony Wolbarst, Kevin](https://reader030.vdocuments.site/reader030/viewer/2022040409/5ec85c40db5591218172f02e/html5/thumbnails/168.jpg)
A Brief Introduction to Magnetic Resonance Imaging
Anthony Wolbarst, Kevin King, Lisa Lemen,
Ron Price, Nathan Yanasak